“Since all terms that are defined are defined by means of other terms, it is clear that human knowledge must always be content to accept some terms as intelligible without definition, in order to have a starting point for its definitions...[and] since human powers are finite, the definitions known to us must always begin somewhere, with terms undefined for the moment, though perhaps not permanently." - Introduction to Mathematical Philosophy”

“We shall be compelled to renounce the hope of finding philosophical proofs of religious beliefs. ...Hence, once more, the value of philosophy must not depend upon any supposed body of definitely ascertainable knowledge to be acquired by those who study it.”

“Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.”

“The beginning of wisdom is the definition of terms.”

“The Church no longer contends that knowledge is in itself sinful, though it did so in its palmy days; but the acquisition of knowledge, even though not sinful, is dangerous, since it may lead to pride of intellect, and hence to a questioning of the Christian dogma.”

“Philosophy arises from an unusually obstinate attempt to arrive at real knowledge. What passes for knowledge in ordinary life suffers from three defects: it is cocksure, vague and self-contradictory. The first step towards philosophy consists in becoming aware of these defects, not in order to rest content with a lazy scepticism, but in order to substitute an amended kind of knowledge which shall be tentative, precise and self-consistent.”

“A truly scientific philosophy will be more humble, more piecemeal, more arduous, offering less glitter of outward mirage to flatter fallacious hopes, but more indifferent to fate, and more capable of accepting the world without the tyrannous imposition of our human and temporary demands.”